# Physical Meaning of complex wavenumber?

• I
• snejburg
In summary, the conversation discusses the physical meaning and energy implications of a complex wavenumber in wave propagation. The medium absorbs the energy of the wave, but the exact mechanism depends on the type of wave and medium. Ultimately, the energy is converted to heat.

#### snejburg

Hey,
This is my first post so I am hoping to do everything right :-)

I do not understand the physical meaning of a complex wavenumber. I understand that, with a general approach u(x,t) = Re(A*[e][(i(kx-omega*t)]) and a complex wavenuber that the wave is decaying exponentially with x. What happens to the energy in that case? In the literature I can only find that the rod (wave propagation in solids) is absorbing all the energy. What kind of energy is it? Thermal energy due to friction (but that is not modeled) or destrucitve interferences (But where is it reflected?)

Thanks for your response,
Jens

snejburg said:
What kind of energy is it?
Photon's energy, it gets absorbed by the medium as the light passes through.
snejburg said:
the rod (wave propagation in solids) is absorbing all the energy.
The medium doesn't have to have the form of a rod. Any medium generally absorbs light to some extent.
snejburg said:
destrucitve interferences (But where is it reflected?)
Interference may happen during light propagation but it doesn't affect the light's total energy.

The OP did not say what kind of wave is he discussing. Maybe a sound wave or EM wave.
The mechanism of absorption depends on the type of wave and the medium. Even for sound waves alone there are several mechanisms for energy dissipation.
In the end it is all heat, but the path to get there may be different.

## What is a complex wavenumber?

A complex wavenumber is a mathematical concept used to describe the propagation of waves in a medium. It is a complex number that combines the properties of a wave's frequency and its propagation speed.

## What is the physical meaning of a complex wavenumber?

The physical meaning of a complex wavenumber is that it represents the attenuation or amplification of a wave as it propagates through a medium. The real part of the complex wavenumber represents the phase change of the wave, while the imaginary part represents the attenuation or amplification of the wave.

## How is the complex wavenumber related to the refractive index?

The complex wavenumber is related to the refractive index by the expression k = nω/c, where k is the complex wavenumber, n is the refractive index, ω is the angular frequency, and c is the speed of light in the medium. This relationship allows for the calculation of the complex wavenumber from the known refractive index of a medium.

## What is the significance of the imaginary part of the complex wavenumber?

The imaginary part of the complex wavenumber is significant because it represents the attenuation or amplification of a wave as it propagates through a medium. This can provide information about the properties and composition of the medium, such as its absorption and scattering characteristics.

## How is the complex wavenumber used in practical applications?

The complex wavenumber is used in various practical applications, such as in the design of optical devices, analysis of electromagnetic fields, and in signal processing. It allows for the characterization and manipulation of waves in different media, providing valuable insights and applications in fields such as optics, acoustics, and telecommunications.